{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LTDQW6N5H7ANJHN2DA36KYHFEX","short_pith_number":"pith:LTDQW6N5","schema_version":"1.0","canonical_sha256":"5cc70b79bd3fc0d49dba1837e560e525f2595360667553a56bfd39aee9deddd2","source":{"kind":"arxiv","id":"1803.04153","version":2},"attestation_state":"computed","paper":{"title":"Local Limit Theorems for Poisson's Binomial in the Case of Infinite Expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Italo Simonelli, Lucia D. Simonelli","submitted_at":"2018-03-12T08:36:15Z","abstract_excerpt":"Let $ V_{n} = X_{1,n} + X_{2,n} + \\cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\\lambda_{n} = \\sum\\limits_{i=1}^{n} b(i;n) $, $\\lambda = \\lim\\limits_{n \\to \\infty} \\lambda_n,$ and $m_n = \\max\\limits_{1 \\leq i \\leq n} b(i;n)$. We derive asymptotic results for $P(V_{n}=k)$ that hold without assuming that $\\lambda < +\\infty$ or $m_n \\to 0$. Also, we do not assume $k$ to be fixed, but instead, our results hold uniformly for all $k$ which satisfy particular growth conditions with respect to $n$. These results extend known P"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.04153","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-12T08:36:15Z","cross_cats_sorted":[],"title_canon_sha256":"ecad7604fc0fd24b155c1be947b26eb0fbacecead37a16daa540cd0f0008f167","abstract_canon_sha256":"47da3474a2b5de90af413afdef7dd907891639af1966afa56197b87181b23e4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:14.500950Z","signature_b64":"GTzaxJ2gE01tDqUrW/JaY6/sVh19SB4/B9TyXA5RGQ8oKhk55Cc1FjqYR0obVPFZnAHJDGQpec2jv+91NhVKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc70b79bd3fc0d49dba1837e560e525f2595360667553a56bfd39aee9deddd2","last_reissued_at":"2026-05-17T23:58:14.500341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:14.500341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Limit Theorems for Poisson's Binomial in the Case of Infinite Expectation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Italo Simonelli, Lucia D. Simonelli","submitted_at":"2018-03-12T08:36:15Z","abstract_excerpt":"Let $ V_{n} = X_{1,n} + X_{2,n} + \\cdots + X_{n,n}$ where $X_{i,n}$ are Bernoulli random variables which take the value $1$ with probability $b(i;n)$. Let $\\lambda_{n} = \\sum\\limits_{i=1}^{n} b(i;n) $, $\\lambda = \\lim\\limits_{n \\to \\infty} \\lambda_n,$ and $m_n = \\max\\limits_{1 \\leq i \\leq n} b(i;n)$. We derive asymptotic results for $P(V_{n}=k)$ that hold without assuming that $\\lambda < +\\infty$ or $m_n \\to 0$. Also, we do not assume $k$ to be fixed, but instead, our results hold uniformly for all $k$ which satisfy particular growth conditions with respect to $n$. These results extend known P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04153","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.04153","created_at":"2026-05-17T23:58:14.500447+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.04153v2","created_at":"2026-05-17T23:58:14.500447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04153","created_at":"2026-05-17T23:58:14.500447+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTDQW6N5H7AN","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTDQW6N5H7ANJHN2","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTDQW6N5","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX","json":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX.json","graph_json":"https://pith.science/api/pith-number/LTDQW6N5H7ANJHN2DA36KYHFEX/graph.json","events_json":"https://pith.science/api/pith-number/LTDQW6N5H7ANJHN2DA36KYHFEX/events.json","paper":"https://pith.science/paper/LTDQW6N5"},"agent_actions":{"view_html":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX","download_json":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX.json","view_paper":"https://pith.science/paper/LTDQW6N5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.04153&json=true","fetch_graph":"https://pith.science/api/pith-number/LTDQW6N5H7ANJHN2DA36KYHFEX/graph.json","fetch_events":"https://pith.science/api/pith-number/LTDQW6N5H7ANJHN2DA36KYHFEX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX/action/storage_attestation","attest_author":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX/action/author_attestation","sign_citation":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX/action/citation_signature","submit_replication":"https://pith.science/pith/LTDQW6N5H7ANJHN2DA36KYHFEX/action/replication_record"}},"created_at":"2026-05-17T23:58:14.500447+00:00","updated_at":"2026-05-17T23:58:14.500447+00:00"}